Hate to disagree on my first post here , but...
Grass clippings are great as a mulch!!
First off they are FREE. Bag 'em, rake 'em dump 'em out on the garden. Sure, they break down fast, but your lawn gets mowed every week, right?
The compost pile is a great spot for the lawn clippings, but in between rows in the garden is good,too. It feeds the soil with organic material as it breaks down, gives the worms and roots a moist cool environment to live in, conserves moisture, suppresses weed germanation and slows erosion.
Yeah, it can heat up if you pile it on thick so don't spread it more than 2-3" thick. It can get slimy and rot if piled on thick and it isn't layered with with a "brown", so top it off with straw.
The method used here is: In between the rows we spread out well rotted horse manure 1/2-1" thick, lay down newspaper 4 or 5 layer thick and overlap all edges, Dump on grass clippings3-4 or 5 " thick, top off with straw 2" deep. Keep piling on grass clippings as it breaks down over the summer to off set the slower-to-rot straw. Dump on shredded leaves in the fall. Side dress rows with compost and weed very little (the newspaper keeps it from germinating).
Next spring it's all worked into the soil by the worms. You won't need a tiller at all and, if you start now, you'll notice a difference by next spring.
I use just grass clippings as a mulch in a raised bed for my garlic. Nuttin' but grass 2" deep...and I need to add more tomorrow...
EDIT: if you use just grass around your tomatoes keep the grass an inch or two away from the stem. Other than that PILE IT ON!!!